Question

A curve passes through the origin of co-ordinates and its gradient is 2x - x^2/3 at the point whose abscissa is x .Find the ordinate of the curve when x = 2

Answer 1

the gradient is\[y'=2x-x^{2/3}\]correct?

Answer 2

@TuringTest yep

Answer 3

integrate to find the formula for y, then plug in x=2

Answer 4

if i integrate i will still have + c

Answer 5

use the fact that the origin is on the curve
this implies that when x=0, y=0
plug that in to you formula after integration and you can solve for C

Answer 6

which means c is 0

Answer 7

correct

Answer 8

thanks i got the way forward..

Answer 9

welcome